P is as efficient as Q and R together. Working together P and Q can complete a work in 18 days and R alone can complete it in 45 days. P and R work together for 12 days, Q alone complete the remaining work in:

16

Let total work = 90

Efficiency P + Q = \(\frac{90}{18}\) = 5   .......(i)

Efficiency of R = \(\frac{90}{45}\) = 2

ATQ,

P's efficiency = (Q + R)'s efficiency

                 P = Q + R

           5 - Q = Q + 2                        from (i)

              2Q = 3 ⇒ Q = 1.5

So, P = Q + R = 1.5 + 2 = 3.5

Here,

Work done by P + R in 12 days = 12 × 5.5 = 66

Remaining work = 90 - 66 = 24

Remaining work done by Q in = \(\frac{24}{1.5}\) = 16 days